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Then, for example, the representation |
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maps to the (unpermuted) representation |
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That is, (A', A")represents the structure  for which |
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In order to examine the effect of dominance on genetic plans, the simple crossover operator must be extended to this new type of representation (inversion takes place, as before, on the individual l-tuples in the homologous pairs). To cross the homologous pair (A', A") with the pair (A"', A""), the procedure will be to cross A' with A''' with probability Pc, and then select one of the resultants at random. Similarly, A" is crossed with A''" and, again, one of the resultants is selected at random. The two selected resultants are then paired to yield one of the outcomes of the extended operation; the other two resultants are paired to yield the other outcome (if it is to be used). |
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To see the effect of dominance on the mutation rate, let us consider the case of two alleles v1, v0 at position i, where v1 is dominant and v0 is recessive. There are four distinct pairs of these alleles which can occur at position i in (A', A"), namely {(v1, v1), (v1, v0), (v0, v1), (v0, v0)}, and only one of these maps to v0 under the dominance map. That is, in the pairs (v1, v0) and (v0, v1) the allele v0 is shielded or stored without test (because the representation maps to one where only allele v1 is present). |
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